The present invention relates to magnetic resonance imaging (MRI) and more particularly to apparatus and methods for quantifying sequence-induced B.sub.0 oscillation and for correcting associated image artifacts.
MRI relies on a stable main magnetic field (B.sub.0) for achieving high spatial resolution and image quality. In a stable field, sequence-controlled field gradients are applied to frequency and/or phase encode the MR signals so that the spatial positions of the signal origins can be determined by analyzing (decoding) the acquired signals. The most commonly used procedures in MRI for signal encoding/decoding are known Fourier methods, such as are described in Kumar, et al., "NMR Fourier Zeugmatography," J. Magn. Reson. 18, 69-83 (1975), and Edelstein, et al., "Spin Warp NMR Imaging and Application to Human Whole-Body Imaging," Phys. Med. Biol. 25, 751-756(1980). In spin-warp imaging techniques, which are the most commonly used Fourier imaging methods in today's practice of MRI, frequency-encoding is achieved by acquiring the signals in the presence of a constant field gradient, and phase-encoding(s) is performed prior to signal acquisition by applying field gradient pulse(s) of fixed duration but with variable strengths.
In practice, however, the B.sub.0 field can be time varying and image artifacts are observed as a result. Such artifacts are described in Henkelman, et al., "Artifacts in Magnetic Resonance Imaging, Rev. Magn. Reson. Med. 2, 1-126 (1987), If the B.sub.0 fluctuation is relatively slow as compared to the readout time (which is usually in the range of tens of milliseconds), image artifacts are dominantly along the phase-encoding direction(s). On the other hand, artifacts may be limited to the readout direction alone when the B.sub.0 fluctuation is sequence-synchronized and the fluctuation is fast relative to the readout time. One example of such sequence-synchronized B.sub.0 fluctuation is the fast oscillating B.sub.0 shift induced by the sequence-controlled field gradient pulses.
Many techniques have been developed to deal with problems related to B.sub.0 instabilities in MRI. Hardware approaches are described in U.S. Pat. Nos. 5,245,286 to Carlson et al., and 5,214,383 to Perlmutter et al. for compensating B.sub.0 fluctuation using magnetometer-type sensors and feed-back circuitry. These approaches, however, require the implementation of additional hardware. The quality of field stabilization achieved by these hardware strategies can be hindered by the noise and lag of the circuitry used.
A different kind of approach involves quantifying the B.sub.0 fluctuation and then using the information during data processing to minimize the influence of B.sub.0 instabilities on the MRI data. Using an electron spin resonator described in U.S. Pat. No. 5,488,950, B.sub.0 fluctuation is quantified with high temporal resolution and is then used for correcting the MRI data to minimize the effects of B.sub.0 instabilities. However, the electron spin resonator method calls for additional hardware sophistication.
Finally, with NMR methods; (such as are described in Yao, et al., "MRI Compensated for Spurious NMR Frequency/Phase Shifts Caused by Spurious Changes in Magnetic Fields During NMR Data Measurement Process," U.S. Pat. No. 4,885,542 (1989); Kaufman, et al., "MRI Compensated For Spurious Rapid Variations in Static Field During a Single MRI sequence," U.S. Pat. No. 4,970,457 (1990) and Zhang, et al., "Correction for Field Variation in Steady-State MRI by Repeated Acquisition of the Zero k-Space Line," U.S. Pat. No. 5,652,514, signals from the nuclear spins being observed are directly sampled to quantify the B.sub.0 time-variation and to guide the data processing for reducing the effects of B.sub.0 instabilities. Since the sampling speed of the previous NMR methods are as slow as or even slower than the readout speed of the MRI data, they become ineffective when the B.sub.0 fluctuation is relatively fast so that image artifacts exist along the readout direction.
The present invention is not; limited to any particular dimensionality of imaging, but for purposes of illustration only two dimensional (2D) cases are presented herein. X is assumed to be the readout direction and Y is assumed to be the phase-encoding direction. B.sub.0 instabilities are assumed to be sequence-synchronized so that the effects are limited to the readout direction only.
FIG. 1 shows a typical spin-warp 2D MRI sequence. A slice of spins are selected by the slice-selective excitation which is achieved by applying a frequency selective radio frequency (RF) pulse in the presence of the slice selection gradient. MR signals are acquired and frequency-encoded during the readout time in the presence of the readout gradient. The phases of the signals are modulated by the application of the phase-encoding gradient which is of fixed duration but with the strength incremented between the projections.
The MRI signal can be described in k-space, according to Twieg, "The k-Trajectory Formulation of the NMR Imaging Process with Applications in Analysis and Synthesis of Imaging Methods," Med. Phys. 10, 610-621(1983), by: ##EQU1## with ##EQU2## and EQU .DELTA.k.sub.y =.gamma..DELTA.G.sub.Y .tau..sub.Y (3)
where M(X,Y) is the spatial distribution of the magnetization to be observed; .DELTA.B.sub.0 (X,Y,t) is the main magnetic field offset as a function of space and time; G.sub.X is the readout gradient; .DELTA.t.sub.X is the readout pitch time; .DELTA.G.sub.Y and .tau..sub.Y are the increment and the duration of the phase-encoding gradient, respectively.
With a stable B.sub.0 field, the field offset .DELTA.B.sub.0 varies only in space. Its effects, in such cases, are limited to shifting the readout spatial frequency, .DELTA.k.sub.X /.DELTA.t.sub.X, by a certain amount which depends on the readout gradient strength and the magnitude of the spatially inhomogeneous B.sub.0 offset. However, a time-varying B.sub.0 field makes the spatial frequency also time dependent. Such frequency variation behaves in the same way as the frequency modulation (FM) in radio communication, causing side bands of the main signals. In MRI, those side bands correspond to image artifacts. As pointed out previously, sequence-synchronization of the B.sub.0 oscillation guarantees that the artifacts exist along only the readout direction.
If the dynamics of the B.sub.0 instabilities are spatially uniform, i.e., with the same frequencies/phases/amplitudes for all spatial positions, the effects of the time variations and the spatial inhomogeneities can be disassociated: EQU .DELTA.B.sub.0 (X,Y,t)=.delta.B.sub.0 (t)+.DELTA.B.sub.0 (X,Y) (4)
In such circumstances, quantification of the B.sub.0 instabilities, .delta.B.sub.0 (t), provides sufficient information for correcting the MRI data to reduce the B.sub.0 instability effects: ##EQU3## where S.sub.Acq stands for the acquired MRI data and S.sub.Corr for the MRI data after being corrected for the B.sub.0 instabilities.